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Stochastic Processes

Strongly Recommended Prerequisites

Recommended Prerequisites

The study of stochastic processes is the application of probability to an indexed collection of random variables. A classic example is the study of queue times, an instance of which is wait times at the post office. Stochastic processes are very important for modeling, but they're also an important tool for other statistical methods. Much of Bayesian statistical estimation is based on Markov chain Monte Carlo, which is a kind of stochastic process.

Recommended Books

Adventures in Stochastic Processes

Sidney I. Resnick

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Key Features

In-text exercises

Key Topics

Absorption Probabilities

Branching Processes

Brownian Motion

Continuous-Time Markov Chains

Discrete State Spaces

Generating Functions

Law of the Iterated Logarithm

Markov Chains

Point Processes

Poisson Process

Queueing

Random Walks

Renewal Theory

Stationary and Limiting Distributions

Stopping Times

Transience and Recurrence

Description

This book has very clear explanations. We particularly appreciate the fact that results are presented in general matrix forms, as opposed to poncing around with the univariate case. Probability exercises tend to be entertaining as data science exercises go, and the antics of Happy Harry in this book are no exception. The asterisked enrichment sections in this book are quite interesting for the more mathematically inclined.

Stochastic Processes

Sheldon M. Ross

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Key Features

In-text exercises

Solutions to some exercises

Key Topics

Birth and Death Processes

Branching Processes

Brownian Motion

Continuous-Time Markov Chains

Hazard Rates

Markov Chains

Martingales

Point Processes

Poisson Approximations

Poisson Process

Probability Review

Queueing

Random Walks

Renewal Reward Processes

Renewal Theory

Stochastic Order Relations

Description

This is the standard text on stochastic processes. We find it somewhat vague in places and some of the results are not presented in as general a form as we would like. However, the exercises are quite good, and the book offers solutions to some of them. It's also geared at a slightly easier level than our top pick, so if you don't have a strong mathematical background you may prefer this book.